Question

If a=√7-√3/√7+√3 and b=√7+√3/√7-√3 find the value of a^2+b^2​

Answer 1

Step-by-step explanation:

a = (√7-√3)/(√7+√3) , b = (√7+√3)/(√7-√3)

→ a = (√7 -√3)(√7 -√3)/(√7+√3)(√7-√3)

→ a = (√7-√3)²/(√7)²-(√3)²

→ a ={ (√7)² +(√3)² -2(√7)(√3)} /7-3

→ a = { 7+3 -2√21}/4

→ a = {10-2√21}/4

→ a = 2{5-√21}/4

→ a = {5-√21}/2

b = (√7+√3)/(√7-√3)

→ b = (√7+√3)(√7+√3)/(√7-√3)(√7+√3)

→ b = (√7+√3)²/(√7)² -(√3)²

→ b ={ (√7)² + (√3)² + 2(√7)(√3) }/ 7-3

→ b = { 7+3+2√21}/4

→ b = {10+2√21}/4

→ b = 2{5+√21}/4

→ b = {5+√21}/2

ATQ

a²+b²

→ [{5-√21}/2]² + [{5+√21}/2]²

→ {5-√21}²/2² + {5+√21}²/2²

→ {5² +(√21)² -2(5)(√21) }/4 + { 5² +(√21)² + 2(5)(√21)/4

→ {25+21-10√21} /4 + {25+ 21 + 10√21}/4

→ {46-10√21}/4 + {46 + 10√21}/4

→ {46-10√21+46+10√21}/4

→ { 46+46}/4

→ 92/4

→ 46/2

→ 23/1

23 is the value of a²+b²